On the State Complexity of Scattered Substrings and Superstrings

Abstract

It is proved that the set of scattered substrings of a language recognized by an n-state DFA requires a DFAwith at least 2 n 2−2 states (the known upper bound is 2), with witness languages given over an exponentially growing alphabet. For a 3-letter alphabet, scattered substrings are shown to require at least 2 √ 2n+30−6 states. A similar state complexity… (More)